The move lends enormous momentum to the years-long push to establish a memorial to women’s history near the National Mall — a proposal that’s lingered in Congress for nearly two decades without ever reaching the president’s desk.

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Congressional supporters from both parties have been working behind the scenes to rally backing and pressure leaders to stage a vote on the bill this year, even as Congress’s shift into campaign mode has left little appetite for most non-essential legislation ahead of November’s midterms.

Cantor spokeswoman Megan Whittemore said the congressman supports the bill and intends to bring it to the floor.

Museum supporters wasted no time praising the announcement, with Rep. Carolyn Maloney — a New York Democrat who’s been working on the proposal since 1998 — saying she’s “thrilled” by Cantor’s move. With top House Democrats already behind the proposal, including House Minority Leader Nancy Pelosi (Calif.) and Minority Whip Steny Hoyer (Md.), Maloney predicted it will sail through the lower chamber.

“This is a huge boost to our efforts,” said Maloney, the bill’s lead sponsor. “Leadership from both parties in the House has now come out in favor of this bill, and I’m hopeful we can secure a large, bipartisan vote in favor of its passage.”

On Tuesday, the House Natural Resources Committee’s subpanel on Public Lands and Environmental Regulation will examine the bill.

The push to create a national women’s history museum comes as the role of women in politics has risen to historic heights, highlighted both by record numbers of women in Congress and the ascension of former Secretary of State Hillary Clinton as a front-runner in the 2016 presidential race — if she chooses to run.

Maloney’s bill would establish a commission charged with examining the best way to bring a women’s history museum “on or near” the National Mall. The eight-member panel, appointed by bipartisan leaders in both the House and Senate, would have 18 months to report recommendations to Congress and the White House for building and maintaining the project.

A Senate companion bill, introduced last year by Sens. Susan Collins (R-Maine) and Barbara Mikulski (D-Md.), has 20 co-sponsors, including 17 of the Senate’s 20 female lawmakers.

Rep. Marsha Blackburn (Tenn.), the House bill’s lead GOP sponsor, said she’s confident the bill will win approval in both chambers this year.

“I do think that it’s the year that it can move on the House floor and the Senate floor,” she said Tuesday by phone. “We’re hopeful that as we move to the spring that we’ll see action on this and make a women’s history museum a reality for the country.”

Using past museum commissions as a guide, the bill’s sponsors estimate the cost of the proposal to be between $1 million and $3 million. They are quick to emphasize that both the commission’s costs and those associated with constructing and maintaining the museum would be funded entirely by private contributions. Actress Meryl Streep has already donated $1 million, Maloney said.

“We know that money’s tight, and that’s why private monies will pay for this memorial, not taxpayer dollars,” Maloney said.

Some Democrats suggested GOP leaders are simply playing election-year politics with the museum bill. One leadership aide said the Republicans would embrace the proposal as a political effort to defuse the Democratic argument that their policy agenda is harmful to women.

“They’re trying to reach out to people other than white males,” the aide said. “They may try to latch onto it to show that they’re not complete Neanderthals.”

It’s unclear what level of opposition the proposal will face on Capitol Hill. The absence of offsets takes away a potential complaint from fiscal hawks, and the GOP’s aggressive effort to be more sensitive to female and minority constituents will likely discourage any significant wave of dissent, even from the most conservative ranks.

Still, Blackburn acknowledged there might be some push-back from those wondering why women should have their own spot on the Mall.

“You’re always going to hear some [say], ‘Well, if we have that, [why don’t] we have a men’s history museum?’ ” she said. “But I think what we have to do is realize that what has been highly recognized in the country is the contribution of men.

“And in part, as they were the elected leaders … that is appropriate,” she added. “But also, there are women who worked alongside them and women who have led great movements in this country, and that should be recognized.”

An earlier version of this story indicated the commission created under the bill would have a year to report recommendations. The timeline is 18 months.